Let T(x, y, z) = 100 + x2 + y2 represent the temperature at each point on the sphere x2 + y2 + z2 = 30. Use Lagrange multipliers to find the maximum temperature on the curve formed by the intersection of the sphere and the plane x - z = 0.

Q: Classify all level curves of f(x, y) = Vy² – x² and draw its contour map.

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Q: 1) The maximum distance from the origin of the xy plane to the circle described by (x – 12)? + (y –…

A: given equation of circlex-122+y-62=16 As per our guideline we supposed to answer only first question…

Q: Suppose ƒ(1, 2) = 4, ƒx(1, 2) = 5, and ƒy(1, 2) = -3. Find an equation of the plane tangent to the…

A: Equation of the plane tangent to the surface  z=f(x, y) at (a, b) is z=fa, b+fxa, b(x-a)+fya, b(y-b)

Q: Describe and sketch the following surfaces z = f(x, y): (a) * (c) 2= /1-x² - y² z = 6 - 2x - 3y (b)…

A: We have to sketch and describe the following curve

Q: Find the equation for the tangent plane to the surface z = - 9x - 7y at the point (2, 1, - 43). O A.…

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Q: 2) Describe the level curves of the surface Z = √36 4X² 9Y²

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Q: Let f(x,y)=/4– 4x² – y² . Find its domain and give a rough sketch of its surface.

A: The given function is:fx, y=4-4x2-y2To find domain and sketch the surface

Q: Sketch a typical level surface for the function f(x,y,z) = 3x² + 3y² + 3z².

A: Given that the function is                       f(x, y, z)=3x2+3y2+3z2.

Q: Find an equation for the surface obtained by rotating the curve y = √ √x about the x-axis.

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